My 1961 English edition of the Larousse Gastronomique seemed a good place to start. On garnitures à la française, it gives this description:
Small nests made from Duchesse potatoes, dipped in egg and breadcrumbs, fried and hollowed out, filled with diced mixed vegetables; bunches of asparagus tips; braised lettuces; flowerets of cauliflower, coated with Hollandaise sauce … [used] for large cuts of meat.
As for sauce à la française , the Larousse quotes Careme (1784-1833), in his Art de la Cuisine Française aud XIXe siècle, noting that this sauce is for fish.
Put into a saucepan some Béchamel sauce based on fish stock. When it is almost boiling, add a little garlic, a little grated nutmeg and mushroom essence. When it has boiled for a moment, and just before serving, add crayfish butter to give it a pinkish colour.
Note: Shelled crayfish tails and small peeled mushrooms may be added to this sauce. I served this sauce for the first time in the house of Prince Paul de Wurtemburg.
Richard Dolby’s The Cook’s Dictionary and Housekeeper’s Directory (1832) includes the following:
Croquignoles à la française:
Break up half a pound of bitter macaroons, so small as to be able to sift them; and having laid half a pound of sifted flour on your slab, and made a hole in the middle, put in the macaroons, with six ounces of powdered sugar, three yolks of eggs, three ounces of fresh butter, and a grain of salt; make these ingredients into a paste, and form the croquignoles of the shape and size of olives; dores them lightly, and bake them in a gentle oven. These must be of a lighter colour than other croquignoles.
Instead of macaroons you may use any other ingredients you please.
In Dainty Dishes from Foreign Lands (1909), the author starts her chapter on Some Delicious French Dishes with the caveat
I do not think that the French have so many distinctive dishes as other nations, but have, rather, a certain style of cooking all things. The recipes which I give, herewith, convey something of the French spirit.
She goes on to single out truffles and mushrooms as being “considered, quite rightly , to distinguish French cookery, but too often they are bedevilled out of all resemblance to their original succulent selves by people who imagine they must be cooked elaborately.” She then provides a few recipes which are simple, and ‘genuinely French.’
Mushrooms with Chicken Livers.
Mushrooms with chicken livers is a dish literally fit for a King; to make it take a dozen (or as many as you want) of chicken livers, and fry them with one or two strips of very thin, very sweet bacon; when the livers are just turning brown, add at least a dozen mushrooms, peeled, and wiped very dry. Simmer five minutes, or until the mushrooms are soft, and serve on hot toast. Into the grease left in the pan drop a tablespoon of flour, and let it brown, stirring constantly. Make this into a gravy by pouring into the pan, very quickly, a cup of cold milk; let it boil up once and pour over the toast, livers, bacon and mushrooms.
And finally, from 365 Foreign Dishes: a foreign dish for every day in the year (1908), a recipe for apple dumplings. I am at a loss to know what the author considered quintessentially French about this dish.
French Baked Apple Dumplings.
Peel and core apples; sprinkle well with sugar. Then mix some cold boiled rice with 1 egg, a pinch of salt, sugar and cinnamon, flour enough to make a dough. Cover the apples with this dough; put in a well-buttered baking dish with 2 tablespoonfuls of butter, and bake to a delicate brown. Serve with whipped cream.
Quotation for the Day.
“Even the coeur flottant merveilleux aux fraises, presented with a great flourish, made little impression, for it was no more than what may happen to the simple, honest dish of strawberries and cream once it falls into the hands of a Frenchman.”
Dr. Watson in 'Sherlock Holmes and the Hapsburg Tiara' by Alan Vanneman (2004)